Problem: $ C = \left[\begin{array}{rrr}4 & 0 & -2 \\ 0 & -1 & 1 \\ 1 & 3 & 1\end{array}\right]$ $ F = \left[\begin{array}{rr}-2 & -2 \\ -1 & 3 \\ 3 & 1\end{array}\right]$ Is $ C- F$ defined?
Explanation: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ C$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ C$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ C$ ) must equal $ q$ (number of columns in $ F$ Do $ C$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ C$ and $ F$ have the same number of columns? No Yes No No Since $ C$ has different dimensions $(3\times3)$ from $ F$ $(3\times2)$, $ C- F$ is not defined.